program main !*****************************************************************************80 ! !! MAIN is the main program for FEM2D_PROJECT. ! ! Discussion: ! ! FEM2D_PROJECT reads files defining a sampling of a (scalar or vector) ! function of 2 arguments, and a list of nodes and triangular elements ! to use for a finite element representation of the data. ! ! It computes a set of finite element coefficients to be associated with ! the given finite element mesh, and writes that information to a file ! so that an FEM representation is formed by the node, element and value ! files. ! ! Usage: ! ! fem2d_project sample_prefix fem_prefix ! ! where 'sample_prefix' is the common prefix for the SAMPLE files: ! ! * sample_prefix_nodes.txt, the node coordinates of samples; ! * sample_prefix_elements.txt, the nodes that make up each element; ! * sample_prefix_values.txt, the sample values. ! ! and 'fem_prefix' is the common prefix for the FEM files: ! ! * fem_prefix_nodes.txt, the node coordinates; ! * fem_prefix_elements.txt, the nodes that make up each element; ! * fem_prefix_values.txt, the values defined at each node, ! computed by this program. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 22 June 2009 ! ! Author: ! ! John Burkardt ! implicit none character ( len = 255 ) fem_element_filename integer ( kind = 4 ), allocatable :: fem_element_node(:,:) integer ( kind = 4 ) fem_element_num integer ( kind = 4 ) fem_element_order integer ( kind = 4 ) fem_node_dim character ( len = 255 ) fem_node_filename integer ( kind = 4 ) fem_node_num real ( kind = 8 ), allocatable :: fem_node_xy(:,:) character ( len = 255 ) fem_prefix real ( kind = 8 ), allocatable :: fem_value(:,:) integer ( kind = 4 ) fem_value_dim character ( len = 255 ) fem_value_filename integer ( kind = 4 ) fem_value_num integer ( kind = 4 ) iarg integer ( kind = 4 ) iargc integer ( kind = 4 ) ios integer ( kind = 4 ) num_arg character ( len = 255 ) sample_element_filename integer ( kind = 4 ), allocatable :: sample_element_neighbor(:,:) integer ( kind = 4 ), allocatable :: sample_element_node(:,:) integer ( kind = 4 ) sample_element_num integer ( kind = 4 ) sample_element_order character ( len = 255 ) sample_prefix integer ( kind = 4 ) sample_node_dim character ( len = 255 ) sample_node_filename integer ( kind = 4 ) sample_node_num real ( kind = 8 ), allocatable :: sample_node_xy(:,:) integer ( kind = 4 ) sample_value_dim integer ( kind = 4 ) sample_value_num real ( kind = 8 ), allocatable :: sample_value(:,:) character ( len = 255 ) sample_value_filename call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT' write ( *, '(a)' ) ' FORTRAN90 version.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) & ' Read files defining a sampling of a function of 2 arguments.' write ( *, '(a)' ) ' Read files defining a finite element mesh.' write ( *, '(a)' ) ' Project the sample data onto the mesh, and' write ( *, '(a)' ) ' write a file of FEM coefficient values.' ! ! Get the number of command line arguments. ! num_arg = iargc ( ) if ( num_arg < 1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'Enter the sample file prefix:' read ( *, '(a)', iostat = ios ) sample_prefix if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' Unexpected read error!' stop end if else iarg = 1 call getarg ( iarg, sample_prefix ) end if if ( num_arg < 2 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'Enter the FEM file prefix:' read ( *, '(a)', iostat = ios ) fem_prefix if ( ios /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' Unexpected read error!' stop end if else iarg = 2 call getarg ( iarg, fem_prefix ) end if ! ! Create the filenames. ! sample_node_filename = trim ( sample_prefix ) // '_nodes.txt' sample_element_filename = trim ( sample_prefix ) // '_elements.txt' sample_value_filename = trim ( sample_prefix ) // '_values.txt' fem_node_filename = trim ( fem_prefix ) // '_nodes.txt' fem_element_filename = trim ( fem_prefix ) // '_elements.txt' fem_value_filename = trim ( fem_prefix ) // '_values.txt' ! ! Read the SAMPLE NODE, ELEMENT and VALUE data. ! call r8mat_header_read ( sample_node_filename, sample_node_dim, & sample_node_num ) allocate ( sample_node_xy(1:sample_node_dim,1:sample_node_num) ) call r8mat_data_read ( sample_node_filename, sample_node_dim, & sample_node_num, sample_node_xy ) write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Sample node spatial dimension is ', sample_node_dim write ( *, '(a,i8)' ) ' Sample node number is ', sample_node_num if ( sample_node_dim /= 2 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' Spatial dimension of the sample nodes is not 2.' stop end if call i4mat_header_read ( sample_element_filename, sample_element_order, & sample_element_num ) allocate ( sample_element_node(1:sample_element_order,1:sample_element_num) ) call i4mat_data_read ( sample_element_filename, sample_element_order, & sample_element_num, sample_element_node ) write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Sample element order is ', sample_element_order write ( *, '(a,i8)' ) ' Sample element number is ', sample_element_num if ( sample_element_order /= 3 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' The sample elements must be of order 3.' stop end if call r8mat_header_read ( sample_value_filename, sample_value_dim, & sample_value_num ) write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Sample value dimension is ', sample_value_dim write ( *, '(a,i8)' ) ' Sample value number is ', sample_value_num if ( sample_value_num /= sample_node_num ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' Number of sample nodes and values are not equal.' stop end if allocate ( sample_value(1:sample_value_dim,1:sample_value_num) ) call r8mat_data_read ( sample_value_filename, sample_value_dim, & sample_value_num, sample_value ) ! ! Create the sample element neighbor array. ! allocate ( sample_element_neighbor(1:3,1:sample_element_num) ) call triangulation_order3_neighbor_triangles ( sample_element_num, & sample_element_node, sample_element_neighbor ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The element neighbor array has been computed.' ! ! Read the FEM NODE and ELEMENT data. ! call r8mat_header_read ( fem_node_filename, fem_node_dim, fem_node_num ) write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' The FEM node dimension is ', fem_node_dim write ( *, '(a,i8)' ) ' The FEM node number is ', fem_node_num if ( fem_node_dim /= 2 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' Spatial dimension of the nodes is not 2.' stop end if allocate ( fem_node_xy(1:fem_node_dim,1:fem_node_num) ) call r8mat_data_read ( fem_node_filename, fem_node_dim, fem_node_num, & fem_node_xy ) call i4mat_header_read ( fem_element_filename, fem_element_order, & fem_element_num ) write ( *, '(a,i8)' ) ' The FEM element order is ', fem_element_order write ( *, '(a,i8)' ) ' The FEM element number is ', fem_element_num if ( fem_element_order /= 3 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' The FEM elements must be of order 3.' stop end if allocate ( fem_element_node(1:fem_element_order,1:fem_element_num) ) call i4mat_data_read ( fem_element_filename, fem_element_order, & fem_element_num, fem_element_node ) ! ! Compute the FEM values. ! fem_value_dim = sample_value_dim fem_value_num = fem_node_num allocate ( fem_value(1:fem_value_dim,1:fem_value_num) ) call fem2d_transfer ( sample_node_num, sample_element_order, & sample_element_num, sample_value_dim, sample_value_num, & sample_node_xy, sample_element_node, sample_element_neighbor, & sample_value, fem_node_num, fem_element_order, & fem_element_num, fem_value_dim, fem_value_num, & fem_node_xy, fem_element_node, fem_value ) ! ! Write the FEM values. ! call r8mat_write ( fem_value_filename, fem_value_dim, & fem_value_num, fem_value ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' FEM value data written to "' & // trim ( fem_value_filename ) // '".' ! ! Free memory. ! deallocate ( fem_element_node ) deallocate ( fem_node_xy ) deallocate ( fem_value ) deallocate ( sample_element_neighbor ) deallocate ( sample_element_node ) deallocate ( sample_node_xy ) deallocate ( sample_value ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop end subroutine basis_mn_t3 ( t, n, p, phi, dphidx, dphidy ) !*****************************************************************************80 ! !! BASIS_MN_T3: all bases at N points for a T3 element. ! ! Discussion: ! ! The routine is given the coordinates of the vertices of a triangle. ! It works directly with these coordinates, and does not refer to a ! reference element. ! ! The sides of the triangle DO NOT have to lie along a coordinate ! axis. ! ! The routine evaluates the basis functions associated with each vertex, ! and their derivatives with respect to X and Y. ! ! Physical Element T3: ! ! 3 ! / \ ! / \ ! / \ ! / \ ! 1---------2 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 08 February 2006 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, real ( kind = 8 ) T(2,3), the coordinates of the vertices ! of the triangle. It is common to list these points in counter clockwise ! order. ! ! Input, integer ( kind = 4 ) N, the number of evaluation points. ! ! Input, real ( kind = 8 ) P(2,N), the points where the basis functions ! are to be evaluated. ! ! Output, real ( kind = 8 ) PHI(3,N), the value of the basis functions ! at the evaluation points. ! ! Output, real ( kind = 8 ) DPHIDX(3,N), DPHIDY(3,N), the value of the ! derivatives at the evaluation points. ! ! Local parameters: ! ! Local, real ( kind = 8 ) AREA, is (twice) the area of the triangle. ! implicit none integer ( kind = 4 ) n real ( kind = 8 ) area real ( kind = 8 ) dphidx(3,n) real ( kind = 8 ) dphidy(3,n) real ( kind = 8 ) p(2,n) real ( kind = 8 ) phi(3,n) real ( kind = 8 ) t(2,3) area = t(1,1) * ( t(2,2) - t(2,3) ) & + t(1,2) * ( t(2,3) - t(2,1) ) & + t(1,3) * ( t(2,1) - t(2,2) ) if ( area == 0.0D+00 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'BASIS_MN_T3 - Fatal error!' write ( *, '(a)' ) ' Element has zero area.' stop end if phi(1,1:n) = ( ( t(1,3) - t(1,2) ) * ( p(2,1:n) - t(2,2) ) & - ( t(2,3) - t(2,2) ) * ( p(1,1:n) - t(1,2) ) ) dphidx(1,1:n) = - ( t(2,3) - t(2,2) ) dphidy(1,1:n) = ( t(1,3) - t(1,2) ) phi(2,1:n) = ( ( t(1,1) - t(1,3) ) * ( p(2,1:n) - t(2,3) ) & - ( t(2,1) - t(2,3) ) * ( p(1,1:n) - t(1,3) ) ) dphidx(2,1:n) = - ( t(2,1) - t(2,3) ) dphidy(2,1:n) = ( t(1,1) - t(1,3) ) phi(3,1:n) = ( ( t(1,2) - t(1,1) ) * ( p(2,1:n) - t(2,1) ) & - ( t(2,2) - t(2,1) ) * ( p(1,1:n) - t(1,1) ) ) dphidx(3,1:n) = - ( t(2,2) - t(2,1) ) dphidy(3,1:n) = ( t(1,2) - t(1,1) ) ! ! Normalize. ! phi(1:3,1:n) = phi(1:3,1:n) / area dphidx(1:3,1:n) = dphidx(1:3,1:n) / area dphidy(1:3,1:n) = dphidy(1:3,1:n) / area return end subroutine basis_mn_t6 ( t, n, p, phi, dphidx, dphidy ) !*****************************************************************************80 ! !! BASIS_MN_T6: all bases at N points for a T6 element. ! ! Discussion: ! ! The routine is given the coordinates of the vertices and midside ! nodes of a triangle. It works directly with these coordinates, and does ! not refer to a reference element. ! ! This routine requires that the midside nodes be "in line" ! with the vertices, that is, that the sides of the triangle be ! straight. However, the midside nodes do not actually have to ! be halfway along the side of the triangle. ! ! Physical element T6: ! ! This picture indicates the assumed ordering of the six nodes ! of the triangle. ! ! 3 ! / \ ! / \ ! 6 5 ! / \ ! / \ ! 1-----4-----2 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 08 February 2006 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, real ( kind = 8 ) T(2,6), the nodal oordinates of the element. ! It is common to list these points in counter clockwise order. ! ! Input, integer ( kind = 4 ) N, the number of evaluation points. ! ! Input, real ( kind = 8 ) P(2,N), the coordinates of the point where ! the basis functions are to be evaluated. ! ! Output, real ( kind = 8 ) PHI(6,N), the basis functions at the ! evaluation points. ! ! Output, real ( kind = 8 ) DPHIDX(6,N), DPHIDY(6,N), the derivatives ! of the basis functions at the evaluation points. ! ! Local Parameters: ! ! Local, real ( kind = 8 ) AREA, is (twice) the area of the triangle. ! implicit none integer ( kind = 4 ) n real ( kind = 8 ) dphidx(6,n) real ( kind = 8 ) dphidy(6,n) real ( kind = 8 ) gn(n) real ( kind = 8 ) gx(n) real ( kind = 8 ) hn(n) real ( kind = 8 ) hx(n) real ( kind = 8 ) p(2,n) real ( kind = 8 ) phi(6,n) real ( kind = 8 ) t(2,6) ! ! Basis function 1: PHI(X,Y) = G(3,2) * H(6,4) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,2) ) * ( t(2,3) - t(2,2) ) & - ( t(1,3) - t(1,2) ) * ( p(2,1:n) - t(2,2) ) gn(1:n) = ( t(1,1) - t(1,2) ) * ( t(2,3) - t(2,2) ) & - ( t(1,3) - t(1,2) ) * ( t(2,1) - t(2,2) ) hx(1:n) = ( p(1,1:n) - t(1,4) ) * ( t(2,6) - t(2,4) ) & - ( t(1,6) - t(1,4) ) * ( p(2,1:n) - t(2,4) ) hn(1:n) = ( t(1,1) - t(1,4) ) * ( t(2,6) - t(2,4) ) & - ( t(1,6) - t(1,4) ) * ( t(2,1) - t(2,4) ) phi(1,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(1,1:n) = ( ( t(2,3) - t(2,2) ) * hx(1:n) & + gx(1:n) * ( t(2,6) - t(2,4) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(1,1:n) = -( ( t(1,3) - t(1,2) ) * hx(1:n) & + gx(1:n) * ( t(1,6) - t(1,4) ) ) / ( gn(1:n) * hn(1:n) ) ! ! Basis function 2: PHI(X,Y) = G(3,1) * H(4,5) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,1) ) * ( t(2,3) - t(2,1) ) & - ( t(1,3) - t(1,1) ) * ( p(2,1:n) - t(2,1) ) gn(1:n) = ( t(1,2) - t(1,1) ) * ( t(2,3) - t(2,1) ) & - ( t(1,3) - t(1,1) ) * ( t(2,2) - t(2,1) ) hx(1:n) = ( p(1,1:n) - t(1,5) ) * ( t(2,4) - t(2,5) ) & - ( t(1,4) - t(1,5) ) * ( p(2,1:n) - t(2,5) ) hn(1:n) = ( t(1,2) - t(1,5) ) * ( t(2,4) - t(2,5) ) & - ( t(1,4) - t(1,5) ) * ( t(2,2) - t(2,5) ) phi(2,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(2,1:n) = ( ( t(2,3) - t(2,1) ) * hx(1:n) & + gx(1:n) * ( t(2,4) - t(2,5) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(2,1:n) = -( ( t(1,3) - t(1,1) ) * hx(1:n) & + gx(1:n) * ( t(1,4) - t(1,5) ) ) / ( gn(1:n) * hn(1:n) ) ! ! Basis function 3: PHI(X,Y) = G(1,2) * H(5,6) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,2) ) * ( t(2,1) - t(2,2) ) & - ( t(1,1) - t(1,2) ) * ( p(2,1:n) - t(2,2) ) gn(1:n) = ( t(1,3) - t(1,2) ) * ( t(2,1) - t(2,2) ) & - ( t(1,1) - t(1,2) ) * ( t(2,3) - t(2,2) ) hx(1:n) = ( p(1,1:n) - t(1,6) ) * ( t(2,5) - t(2,6) ) & - ( t(1,5) - t(1,6) ) * ( p(2,1:n) - t(2,6) ) hn(1:n) = ( t(1,3) - t(1,6) ) * ( t(2,5) - t(2,6) ) & - ( t(1,5) - t(1,6) ) * ( t(2,3) - t(2,6) ) phi(3,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(3,1:n) = ( ( t(2,1) - t(2,2) ) * hx(1:n) & + gx(1:n) * ( t(2,5) - t(2,6) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(3,1:n) = -( ( t(1,1) - t(1,2) ) * hx(1:n) & + gx(1:n) * ( t(1,5) - t(1,6) ) ) / ( gn(1:n) * hn(1:n) ) ! ! Basis function 4: PHI(X,Y) = G(1,3) * H(2,3) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,3) ) * ( t(2,1) - t(2,3) ) & - ( t(1,1) - t(1,3) ) * ( p(2,1:n) - t(2,3) ) gn(1:n) = ( t(1,4) - t(1,3) ) * ( t(2,1) - t(2,3) ) & - ( t(1,1) - t(1,3) ) * ( t(2,4) - t(2,3) ) hx(1:n) = ( p(1,1:n) - t(1,3) ) * ( t(2,2) - t(2,3) ) & - ( t(1,2) - t(1,3) ) * ( p(2,1:n) - t(2,3) ) hn(1:n) = ( t(1,4) - t(1,3) ) * ( t(2,2) - t(2,3) ) & - ( t(1,2) - t(1,3) ) * ( t(2,4) - t(2,3) ) phi(4,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(4,1:n) = ( ( t(2,1) - t(2,3) ) * hx(1:n) & + gx(1:n) * ( t(2,2) - t(2,3) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(4,1:n) = -( ( t(1,1) - t(1,3) ) * hx(1:n) & + gx(1:n) * ( t(1,2) - t(1,3) ) ) / ( gn(1:n) * hn(1:n) ) ! ! Basis function 5: PHI(X,Y) = G(2,1) * H(3,1) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,1) ) * ( t(2,2) - t(2,1) ) & - ( t(1,2) - t(1,1) ) * ( p(2,1:n) - t(2,1) ) gn(1:n) = ( t(1,5) - t(1,1) ) * ( t(2,2) - t(2,1) ) & - ( t(1,2) - t(1,1) ) * ( t(2,5) - t(2,1) ) hx(1:n) = ( p(1,1:n) - t(1,1) ) * ( t(2,3) - t(2,1) ) & - ( t(1,3) - t(1,1) ) * ( p(2,1:n) - t(2,1) ) hn(1:n) = ( t(1,5) - t(1,1) ) * ( t(2,3) - t(2,1) ) & - ( t(1,3) - t(1,1) ) * ( t(2,5) - t(2,1) ) phi(5,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(5,1:n) = ( ( t(2,2) - t(2,1) ) * hx(1:n) & + gx(1:n) * ( t(2,3) - t(2,1) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(5,1:n) = -( ( t(1,2) - t(1,1) ) * hx(1:n) & + gx(1:n) * ( t(1,3) - t(1,1) ) ) / ( gn(1:n) * hn(1:n) ) ! ! Basis function 6: PHI(X,Y) = G(1,2) * H(3,2) / normalization. ! gx(1:n) = ( p(1,1:n) - t(1,2) ) * ( t(2,1) - t(2,2) ) & - ( t(1,1) - t(1,2) ) * ( p(2,1:n) - t(2,2) ) gn(1:n) = ( t(1,6) - t(1,2) ) * ( t(2,1) - t(2,2) ) & - ( t(1,1) - t(1,2) ) * ( t(2,6) - t(2,2) ) hx(1:n) = ( p(1,1:n) - t(1,2) ) * ( t(2,3) - t(2,2) ) & - ( t(1,3) - t(1,2) ) * ( p(2,1:n) - t(2,2) ) hn(1:n) = ( t(1,6) - t(1,2) ) * ( t(2,3) - t(2,2) ) & - ( t(1,3) - t(1,2) ) * ( t(2,6) - t(2,2) ) phi(6,1:n) = ( gx(1:n) * hx(1:n) ) / ( gn(1:n) * hn(1:n) ) dphidx(6,1:n) = ( ( t(2,1) - t(2,2) ) * hx(1:n) & + gx(1:n) * ( t(2,3) - t(2,2) ) ) / ( gn(1:n) * hn(1:n) ) dphidy(6,1:n) = -( ( t(1,1) - t(1,2) ) * hx(1:n) & + gx(1:n) * ( t(1,3) - t(1,2) ) ) / ( gn(1:n) * hn(1:n) ) return end subroutine ch_cap ( c ) !*****************************************************************************80 ! !! CH_CAP capitalizes a single character. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 19 July 1998 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input/output, character C, the character to capitalize. ! implicit none character c integer ( kind = 4 ) itemp itemp = ichar ( c ) if ( 97 <= itemp .and. itemp <= 122 ) then c = char ( itemp - 32 ) end if return end function ch_eqi ( c1, c2 ) !*****************************************************************************80 ! !! CH_EQI is a case insensitive comparison of two characters for equality. ! ! Example: ! ! CH_EQI ( 'A', 'a' ) is .TRUE. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 28 July 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C1, C2, the characters to compare. ! ! Output, logical CH_EQI, the result of the comparison. ! implicit none logical ch_eqi character c1 character c1_cap character c2 character c2_cap c1_cap = c1 c2_cap = c2 call ch_cap ( c1_cap ) call ch_cap ( c2_cap ) if ( c1_cap == c2_cap ) then ch_eqi = .true. else ch_eqi = .false. end if return end subroutine ch_to_digit ( c, digit ) !*****************************************************************************80 ! !! CH_TO_DIGIT returns the value of a base 10 digit. ! ! Example: ! ! C DIGIT ! --- ----- ! '0' 0 ! '1' 1 ! ... ... ! '9' 9 ! ' ' 0 ! 'X' -1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 August 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character C, the decimal digit, '0' through '9' or blank ! are legal. ! ! Output, integer ( kind = 4 ) DIGIT, the corresponding value. ! If C was 'illegal', then DIGIT is -1. ! implicit none character c integer ( kind = 4 ) digit if ( lge ( c, '0' ) .and. lle ( c, '9' ) ) then digit = ichar ( c ) - 48 else if ( c == ' ' ) then digit = 0 else digit = -1 end if return end subroutine fem2d_transfer ( sample_node_num, sample_element_order, & sample_element_num, sample_value_dim, sample_value_num, & sample_node_xy, sample_element_node, sample_element_neighbor, sample_value, & fem_node_num, fem_element_order, & fem_element_num, fem_value_dim, fem_value_num, & fem_node_xy, fem_element_node, fem_value ) !*****************************************************************************80 ! !! FEM2D_TRANSFER "transfers" from one finite element mesh to another. ! ! BAD THINGS: ! ! 1) the linear system A*X=B is defined with A being a full storage matrix. ! 2) the quadrature rule used is low order. ! 3) the triangular elements are assumed to be linear. ! ! Discussion: ! ! We are also given a set of "sample" finite element function defined ! by SAMPLE_NODE_XY, SAMPLE_ELEMENT, and SAMPLE_VALUE. ! ! We are given a second finite element mesh, FEM_NODE_XY and ! FEM_ELEMENT_NODE. ! ! Our aim is to "project" the sample data values into the finite element ! space, that is, to come up with a finite element function FEM_VALUE which ! well approximates the sample data. ! ! Now let W(x,y) represent a function interpolating the sample data, and ! let Vk(x,y) represent the finite element basis function associated with ! node K. ! ! Then we seek the coefficient vector U corresponding to a finite element ! function U(x,y) of the form: ! ! U(x,y) = sum ( 1 <= K <= N ) Uk * Vk(x,y) ! ! To determine the coefficent vector entries U, we form a set of ! projection equations. For node K at grid point (I,J), the associated ! basis function Vk(x,y) is used to pose the equation: ! ! Integral U(x,y) Vk(x,y) dx dy = Integral W(x,y) Vk(x,y) dx dy ! ! The left hand side is the usual stiffness matrix times the desired ! coefficient vector U. To complete the system, we simply need to ! determine the right hand side, that is, the integral of the data function ! W against the basis function Vk. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 30 June 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) SAMPLE_NODE_NUM, the number of nodes. ! ! Input, integer ( kind = 4 ) SAMPLE_ELEMENT_ORDER, the element order. ! ! Input, integer ( kind = 4 ) SAMPLE_ELEMENT_NUM, the number of elements. ! ! Input, integer ( kind = 4 ) SAMPLE_VALUE_DIM, the value dimension. ! ! Input, integer ( kind = 4 ) SAMPLE_VALUE_NUM, the number of values. ! ! Input, real ( kind = 8 ) SAMPLE_NODE_XY(2,SAMPLE_NODE_NUM), the nodes. ! ! Input, integer ( kind = 4 ) ! SAMPLE_ELEMENT_NODE(SAMPLE_ELEMENT_ORDER,SAMPLE_ELEMENT_NUM), ! the nodes that make up each element. ! ! Input, integer ( kind = 4 ) SAMPLE_ELEMENT_NEIGHBOR(3,SAMPLE_ELEMENT_NUM), ! the neighbor triangles. ! ! Input, real ( kind = 8 ) SAMPLE_VALUE(SAMPLE_VALUE_DIM,SAMPLE_NODE_NUM), ! the values. ! ! Input, integer ( kind = 4 ) FEM_NODE_NUM, the number of nodes. ! ! Input, integer ( kind = 4 ) FEM_ELEMENT_ORDER, the element order. ! ! Input, integer ( kind = 4 ) FEM_ELEMENT_NUM, the number of elements. ! ! Input, integer ( kind = 4 ) FEM_VALUE_DIM, the value dimension. ! ! Input, integer ( kind = 4 ) FEM_VALUE_NUM, the number of values. ! ! Input, real ( kind = 8 ) FEM_NODE_XY(2,FEM_NODE_NUM), the nodes. ! ! Input, integer ( kind = 4 ) ! FEM_ELEMENT_NODE(FEM_ELEMENT_ORDER,FEM_ELEMENT_NUM), ! the nodes that make up each element. ! ! Output, real ( kind = 8 ) FEM_VALUE(FEM_VALUE_DIM,FEM_VALUE_NUM), ! the values. ! implicit none integer ( kind = 4 ) fem_element_num integer ( kind = 4 ) fem_element_order integer ( kind = 4 ) fem_node_num integer ( kind = 4 ) fem_value_dim integer ( kind = 4 ) fem_value_num integer ( kind = 4 ) sample_element_num integer ( kind = 4 ) sample_element_order integer ( kind = 4 ) sample_node_num integer ( kind = 4 ) sample_value_dim integer ( kind = 4 ) sample_value_num real ( kind = 8 ), allocatable, dimension (:,:) :: a real ( kind = 8 ) area real ( kind = 8 ), allocatable, dimension (:,:) :: b integer ( kind = 4 ) element integer ( kind = 4 ) fem_element_node(fem_element_order,fem_element_num) real ( kind = 8 ) fem_node_xy(2,fem_node_num) real ( kind = 8 ) fem_value(fem_value_dim,fem_value_num) integer ( kind = 4 ) i1 integer ( kind = 4 ) i2 integer ( kind = 4 ) i3 integer ( kind = 4 ) info integer ( kind = 4 ) nq1 integer ( kind = 4 ) nq2 integer ( kind = 4 ) nti1 integer ( kind = 4 ) nti2 integer ( kind = 4 ) nti3 integer ( kind = 4 ) ntj1 integer ( kind = 4 ) ntj2 integer ( kind = 4 ) ntj3 integer ( kind = 4 ), parameter :: project_node_num = 1 real ( kind = 8 ) project_node_xy(2,1) real ( kind = 8 ) project_value(fem_value_dim,1) integer ( kind = 4 ) q1 integer ( kind = 4 ) q2 real ( kind = 8 ) qi real ( kind = 8 ) qj integer ( kind = 4 ) quad integer ( kind = 4 ), parameter :: quad_num = 3 integer ( kind = 4 ) sample_element_neighbor(3,sample_element_num) integer ( kind = 4 ) & sample_element_node(sample_element_order,sample_element_num) real ( kind = 8 ) sample_node_xy(2,sample_node_num) real ( kind = 8 ) sample_value(sample_value_dim,sample_node_num) integer ( kind = 4 ) ti1 integer ( kind = 4 ) ti2 integer ( kind = 4 ) ti3 integer ( kind = 4 ) tj1 integer ( kind = 4 ) tj2 integer ( kind = 4 ) tj3 real ( kind = 8 ) w real ( kind = 8 ) wq real ( kind = 8 ) xq real ( kind = 8 ) yq ! ! Assemble the coefficient matrix A and the right-hand side B. ! allocate ( b(1:fem_node_num,1:fem_value_dim) ) allocate ( a(1:fem_node_num,1:fem_node_num) ) b(1:fem_node_num,1:fem_value_dim) = 0.0D+00 a(1:fem_node_num,1:fem_node_num) = 0.0D+00 do element = 1, fem_element_num i1 = fem_element_node(1,element) i2 = fem_element_node(2,element) i3 = fem_element_node(3,element) area = 0.5D+00 * & ( fem_node_xy(1,i1) * ( fem_node_xy(2,i2) - fem_node_xy(2,i3) ) & + fem_node_xy(1,i2) * ( fem_node_xy(2,i3) - fem_node_xy(2,i1) ) & + fem_node_xy(1,i3) * ( fem_node_xy(2,i1) - fem_node_xy(2,i2) ) ) ! ! Consider each quadrature point. ! Here, we use the midside nodes as quadrature points. ! do quad = 1, quad_num q1 = quad q2 = mod ( quad, quad_num ) + 1 nq1 = fem_element_node(q1,element) nq2 = fem_element_node(q2,element) xq = 0.5D+00 * ( fem_node_xy(1,nq1) + fem_node_xy(1,nq2) ) yq = 0.5D+00 * ( fem_node_xy(2,nq1) + fem_node_xy(2,nq2) ) wq = 1.0D+00 / 3.0D+00 ! ! Consider each test function in the element. ! do ti1 = 1, 3 ti2 = mod ( ti1, 3 ) + 1 ti3 = mod ( ti1 + 1, 3 ) + 1 nti1 = fem_element_node(ti1,element) nti2 = fem_element_node(ti2,element) nti3 = fem_element_node(ti3,element) qi = 0.5D+00 * ( & ( fem_node_xy(1,nti3) - fem_node_xy(1,nti2) ) & * ( yq - fem_node_xy(2,nti2) ) & - ( fem_node_xy(2,nti3) - fem_node_xy(2,nti2) ) & * ( xq - fem_node_xy(1,nti2) ) ) / area ! ! The projection takes place here. The finite element code needs the value ! of the sample function at the point (XQ,YQ). The call to PROJECTION ! locates (XQ,YQ) in the triangulated mesh of sample data, and returns a ! value produced by piecewise linear interpolation. ! project_node_xy(1:2,1) = (/ xq, yq /) call projection ( sample_node_num, sample_node_xy, & sample_element_order, sample_element_num, sample_element_node, & sample_element_neighbor, sample_value_dim, sample_value, & project_node_num, project_node_xy, project_value ) b(nti1,1:fem_value_dim) = b(nti1,1:fem_value_dim) & + area * wq * ( project_value(1:fem_value_dim,1) * qi ) ! ! Consider each basis function in the element. ! do tj1 = 1, 3 tj2 = mod ( tj1, 3 ) + 1 tj3 = mod ( tj1 + 1, 3 ) + 1 ntj1 = fem_element_node(tj1,element) ntj2 = fem_element_node(tj2,element) ntj3 = fem_element_node(tj3,element) qj = 0.5D+00 * ( & ( fem_node_xy(1,ntj3) - fem_node_xy(1,ntj2) ) & * ( yq - fem_node_xy(2,ntj2) ) & - ( fem_node_xy(2,ntj3) - fem_node_xy(2,ntj2) ) & * ( xq - fem_node_xy(1,ntj2) ) ) / area a(nti1,ntj1) = a(nti1,ntj1) + area * wq * ( qi * qj ) end do end do end do end do ! ! SOLVE the linear system A * X = B. ! ! The solution X is actually returned in the space occupied by B. ! call r8ge_fss ( fem_node_num, a, fem_value_dim, b, info ) if ( info /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FEM2D_PROJECT - Fatal error!' write ( *, '(a)' ) ' R8GEFS returned an error condition.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The linear system was not solved, and the' write ( *, '(a)' ) ' algorithm cannot proceed.' stop end if ! ! Copy solution. ! fem_value(1:fem_value_dim,1:fem_value_num) = transpose ( b ) deallocate ( a ) deallocate ( b ) return end subroutine file_column_count ( input_file_name, column_num ) !*****************************************************************************80 ! !! FILE_COLUMN_COUNT counts the number of columns in the first line of a file. ! ! Discussion: ! ! The file is assumed to be a simple text file. ! ! Most lines of the file is presumed to consist of COLUMN_NUM words, ! separated by spaces. There may also be some blank lines, and some ! comment lines, ! which have a "#" in column 1. ! ! The routine tries to find the first non-comment non-blank line and ! counts the number of words in that line. ! ! If all lines are blanks or comments, it goes back and tries to analyze ! a comment line. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 21 June 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the file. ! ! Output, integer ( kind = 4 ) COLUMN_NUM, the number of columns in the file. ! implicit none integer ( kind = 4 ) column_num logical got_one character ( len = * ) input_file_name integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit character ( len = 255 ) line ! ! Open the file. ! call get_unit ( input_unit ) open ( unit = input_unit, file = input_file_name, status = 'old', & form = 'formatted', access = 'sequential', iostat = input_status ) if ( input_status /= 0 ) then column_num = -1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_COLUMN_COUNT - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' & // trim ( input_file_name ) // '" on unit ', input_unit return end if ! ! Read one line, but skip blank lines and comment lines. ! got_one = .false. do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then exit end if if ( len_trim ( line ) == 0 ) then cycle end if if ( line(1:1) == '#' ) then cycle end if got_one = .true. exit end do if ( .not. got_one ) then rewind ( input_unit ) do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then exit end if if ( len_trim ( line ) == 0 ) then cycle end if got_one = .true. exit end do end if close ( unit = input_unit ) if ( .not. got_one ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_COLUMN_COUNT - Warning!' write ( *, '(a)' ) ' The file does not seem to contain any data.' column_num = -1 return end if call s_word_count ( line, column_num ) return end subroutine file_row_count ( input_file_name, row_num ) !*****************************************************************************80 ! !! FILE_ROW_COUNT counts the number of row records in a file. ! ! Discussion: ! ! It does not count lines that are blank, or that begin with a ! comment symbol '#'. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 06 March 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the input file. ! ! Output, integer ( kind = 4 ) ROW_NUM, the number of rows found. ! implicit none integer ( kind = 4 ) bad_num integer ( kind = 4 ) comment_num integer ( kind = 4 ) ierror character ( len = * ) input_file_name integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit character ( len = 255 ) line integer ( kind = 4 ) record_num integer ( kind = 4 ) row_num call get_unit ( input_unit ) open ( unit = input_unit, file = input_file_name, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then row_num = -1; ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'FILE_ROW_COUNT - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_file_name ) // '" on unit ', input_unit stop end if comment_num = 0 row_num = 0 record_num = 0 bad_num = 0 do read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then ierror = record_num exit end if record_num = record_num + 1 if ( line(1:1) == '#' ) then comment_num = comment_num + 1 cycle end if if ( len_trim ( line ) == 0 ) then comment_num = comment_num + 1 cycle end if row_num = row_num + 1 end do close ( unit = input_unit ) return end subroutine get_unit ( iunit ) !*****************************************************************************80 ! !! GET_UNIT returns a free FORTRAN unit number. ! ! Discussion: ! ! A "free" FORTRAN unit number is an integer between 1 and 99 which ! is not currently associated with an I/O device. A free FORTRAN unit ! number is needed in order to open a file with the OPEN command. ! ! If IUNIT = 0, then no free FORTRAN unit could be found, although ! all 99 units were checked (except for units 5, 6 and 9, which ! are commonly reserved for console I/O). ! ! Otherwise, IUNIT is an integer between 1 and 99, representing a ! free FORTRAN unit. Note that GET_UNIT assumes that units 5 and 6 ! are special, and will never return those values. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 26 October 2008 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer ( kind = 4 ) IUNIT, the free unit number. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ) ios integer ( kind = 4 ) iunit logical lopen iunit = 0 do i = 1, 99 if ( i /= 5 .and. i /= 6 .and. i /= 9 ) then inquire ( unit = i, opened = lopen, iostat = ios ) if ( ios == 0 ) then if ( .not. lopen ) then iunit = i return end if end if end if end do return end subroutine i4col_compare ( m, n, a, i, j, isgn ) !*****************************************************************************80 ! !! I4COL_COMPARE compares columns I and J of an I4COL. ! ! Example: ! ! Input: ! ! M = 3, N = 4, I = 2, J = 4 ! ! A = ( ! 1 2 3 4 ! 5 6 7 8 ! 9 10 11 12 ) ! ! Output: ! ! ISGN = -1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 30 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns. ! ! Input, integer ( kind = 4 ) A(M,N), an array of N columns of vectors ! of length M. ! ! Input, integer ( kind = 4 ) I, J, the columns to be compared. ! I and J must be between 1 and N. ! ! Output, integer ( kind = 4 ) ISGN, the results of the comparison: ! -1, column I < column J, ! 0, column I = column J, ! +1, column J < column I. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) i integer ( kind = 4 ) isgn integer ( kind = 4 ) j integer ( kind = 4 ) k ! ! Check. ! if ( i < 1 .or. n < i ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4COL_COMPARE - Fatal error!' write ( *, '(a)' ) ' Column index I is out of bounds.' stop end if if ( j < 1 .or. n < j ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4COL_COMPARE - Fatal error!' write ( *, '(a)' ) ' Column index J is out of bounds.' stop end if isgn = 0 if ( i == j ) then return end if k = 1 do while ( k <= m ) if ( a(k,i) < a(k,j) ) then isgn = -1 return else if ( a(k,j) < a(k,i) ) then isgn = +1 return end if k = k + 1 end do return end subroutine i4col_sort_a ( m, n, a ) !*****************************************************************************80 ! !! I4COL_SORT_A ascending sorts an I4COL. ! ! Discussion: ! ! In lexicographic order, the statement "X < Y", applied to two real ! vectors X and Y of length M, means that there is some index I, with ! 1 <= I <= M, with the property that ! ! X(J) = Y(J) for J < I, ! and ! X(I) < Y(I). ! ! In other words, the first time they differ, X is smaller. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 25 September 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, the number of rows of A, and the length of ! a vector of data. ! ! Input, integer ( kind = 4 ) N, the number of columns of A. ! ! Input/output, integer ( kind = 4 ) A(M,N). ! On input, the array of N columns of M-vectors. ! On output, the columns of A have been sorted in ascending ! lexicographic order. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) i integer ( kind = 4 ) indx integer ( kind = 4 ) isgn integer ( kind = 4 ) j if ( m <= 0 ) then return end if if ( n <= 1 ) then return end if ! ! Initialize. ! i = 0 indx = 0 isgn = 0 j = 0 ! ! Call the external heap sorter. ! do call sort_heap_external ( n, indx, i, j, isgn ) ! ! Interchange the I and J objects. ! if ( 0 < indx ) then call i4col_swap ( m, n, a, i, j ) ! ! Compare the I and J objects. ! else if ( indx < 0 ) then call i4col_compare ( m, n, a, i, j, isgn ) else if ( indx == 0 ) then exit end if end do return end subroutine i4col_swap ( m, n, a, i, j ) !*****************************************************************************80 ! !! I4COL_SWAP swaps columns I and J of an I4COL. ! ! Example: ! ! Input: ! ! M = 3, N = 4, I = 2, J = 4 ! ! A = ( ! 1 2 3 4 ! 5 6 7 8 ! 9 10 11 12 ) ! ! Output: ! ! A = ( ! 1 4 3 2 ! 5 8 7 6 ! 9 12 11 10 ) ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 April 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) M, N, the number of rows and columns ! in the array. ! ! Input/output, integer ( kind = 4 ) A(M,N), an array of N columns ! of length M. ! ! Input, integer ( kind = 4 ) I, J, the columns to be swapped. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) a(m,n) integer ( kind = 4 ) col(m) integer ( kind = 4 ) i integer ( kind = 4 ) j if ( i < 1 .or. n < i .or. j < 1 .or. n < j ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4COL_SWAP - Fatal error!' write ( *, '(a)' ) ' I or J is out of bounds.' write ( *, '(a,i8)' ) ' I = ', i write ( *, '(a,i8)' ) ' J = ', j write ( *, '(a,i8)' ) ' N = ', n stop end if if ( i == j ) then return end if col(1:m) = a(1:m,i) a(1:m,i) = a(1:m,j) a(1:m,j) = col(1:m) return end subroutine i4mat_data_read ( input_file_name, m, n, table ) !*****************************************************************************80 ! !! I4MAT_DATA_READ reads data from an I4MAT file. ! ! Discussion: ! ! The file may contain more than N points, but this routine ! will return after reading N points. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 27 January 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the input file. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Output, integer ( kind = 4 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) ierror character ( len = * ) input_file_name integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit integer ( kind = 4 ) j character ( len = 255 ) line integer ( kind = 4 ) table(m,n) integer ( kind = 4 ) x(m) ierror = 0 call get_unit ( input_unit ) open ( unit = input_unit, file = input_file_name, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_DATA_READ - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_file_name ) // '" on unit ', input_unit stop end if j = 0 do while ( j < n ) read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then ierror = 2 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_DATA_READ - Fatal error!' write ( *, '(a)' ) ' Error while reading lines of data.' write ( *, '(a,i8)' ) ' Number of values expected per line M = ', m write ( *, '(a,i8)' ) ' Number of data lines read, J = ', j write ( *, '(a,i8)' ) ' Number of data lines needed, N = ', n stop end if if ( line(1:1) == '#' .or. len_trim ( line ) == 0 ) then cycle end if call s_to_i4vec ( line, m, x, ierror ) if ( ierror /= 0 ) then cycle end if j = j + 1 table(1:m,j) = x(1:m) end do close ( unit = input_unit ) return end subroutine i4mat_header_read ( input_file_name, m, n ) !*****************************************************************************80 ! !! I4MAT_HEADER_READ reads the header from an I4MAT. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 04 June 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the input file. ! ! Output, integer ( kind = 4 ) M, spatial dimension. ! ! Output, integer ( kind = 4 ) N, the number of points. ! implicit none character ( len = * ) input_file_name integer ( kind = 4 ) m integer ( kind = 4 ) n call file_column_count ( input_file_name, m ) if ( m <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data columns in' write ( *, '(a)' ) ' the file "' // trim ( input_file_name ) // '".' stop end if call file_row_count ( input_file_name, n ) if ( n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I4MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data rows in' write ( *, '(a)' ) ' the file "' // trim ( input_file_name ) // '".' stop end if return end subroutine projection ( fem_node_num, fem_node_xy, fem_element_order, & fem_element_num, fem_element_node, fem_element_neighbor, fem_value_dim, & fem_value, sample_node_num, sample_node_xy, sample_value ) !*****************************************************************************80 ! !! PROJECTION evaluates an FEM function on a T3 or T6 triangulation. ! ! Discussion: ! ! Note that the sample values returned are true values of the underlying ! finite element function. They are NOT produced by constructing some ! other function that interpolates the data at the finite element nodes ! (something which MATLAB's griddata function can easily do.) Instead, ! each sampling node is located within one of the associated finite ! element triangles, and the finite element function is developed and ! evaluated there. ! ! MATLAB's scattered data interpolation is wonderful, but it cannot ! be guaranteed to reproduce the finite element function corresponding ! to nodal data. This routine can (or at least tries to!). ! ! So if you are using finite elements, then using THIS routine ! (but not MATLAB's griddata function), what you see is what you have! ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 01 August 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) FEM_NODE_NUM, the number of nodes. ! ! Input, real ( kind = 8 ) FEM_NODE_XY(2,FEM_NODE_NUM), the coordinates ! of the nodes. ! ! Input, integer ( kind = 4 ) FEM_ELEMENT_ORDER, the order of the elements, ! either 3 or 6. ! ! Input, integer ( kind = 4 ) FEM_ELEMENT_NUM, the number of elements. ! ! Input, integer ( kind = 4 ) ! FEM_ELEMENT_NODE(FEM_ELEMENT_ORDER,FEM_ELEMENT_NUM), the ! nodes that make up each element. ! ! Input, integer ( kind = 4 ) FEM_ELEMENT_NEIGHBOR(3,FEM_ELEMENT_NUM), the ! index of the neighboring element on each side, or -1 if no neighbor there. ! ! Input, integer ( kind = 4 ) FEM_VALUE_DIM, the "dimension" of the values. ! ! Input, real ( kind = 8 ) FEM_VALUE(FEM_VALUE_DIM,FEM_NODE_NUM), the ! finite element coefficient values at each node. ! ! Input, integer ( kind = 4 ) SAMPLE_NODE_NUM, the number of sample nodes. ! ! Input, real ( kind = 8 ) SAMPLE_NODE_XY(2,SAMPLE_NODE_NUM), ! the sample nodes. ! ! Output, real ( kind = 8 ) SAMPLE_VALUE(FEM_VALUE_DIM,SAMPLE_NODE_NUM), ! the sampled values. ! implicit none integer ( kind = 4 ) fem_element_num integer ( kind = 4 ) fem_element_order integer ( kind = 4 ) fem_node_num integer ( kind = 4 ) fem_value_dim integer ( kind = 4 ) sample_node_num real ( kind = 8 ) b(fem_element_order) real ( kind = 8 ) dbdx(fem_element_order) real ( kind = 8 ) dbdy(fem_element_order) integer ( kind = 4 ) edge integer ( kind = 4 ) fem_element_neighbor(3,fem_element_num) integer ( kind = 4 ) fem_element_node(fem_element_order,fem_element_num) real ( kind = 8 ) fem_node_xy(2,fem_node_num) real ( kind = 8 ) fem_value(fem_value_dim,fem_node_num) integer ( kind = 4 ) i integer ( kind = 4 ) j real ( kind = 8 ), dimension ( 2 ) :: p_xy real ( kind = 8 ) sample_node_xy(2,sample_node_num) real ( kind = 8 ) sample_value(fem_value_dim,sample_node_num) integer ( kind = 4 ) t integer ( kind = 4 ) t_node(fem_element_order) real ( kind = 8 ) t_xy(2,fem_element_order) ! ! For each sample point, find the element T that contains it, ! and evaluate the finite element function there. ! do j = 1, sample_node_num p_xy(1:2) = sample_node_xy(1:2,j) ! ! Find the element T that contains the point. ! call triangulation_search_delaunay ( fem_node_num, fem_node_xy, & fem_element_order, fem_element_num, fem_element_node, & fem_element_neighbor, p_xy, t, edge ) if ( t == -1 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'PROJECTION - Fatal error!' write ( *, '(a)' ) ' Triangulation search failed.' stop end if ! ! Evaluate the finite element basis functions at the point in T. ! t_node(1:fem_element_order) = fem_element_node(1:fem_element_order,t) t_xy(1:2,1:fem_element_order) = fem_node_xy(1:2,t_node(1:fem_element_order)) if ( fem_element_order == 3 ) then call basis_mn_t3 ( t_xy, 1, p_xy, b, dbdx, dbdy ) else if ( fem_element_order == 6 ) then call basis_mn_t6 ( t_xy, 1, p_xy, b, dbdx, dbdy ) end if ! ! Multiply by the finite element values to get the sample values. ! do i = 1, fem_value_dim sample_value(i,j) = dot_product ( & fem_value(i,t_node(1:fem_element_order)), b(1:fem_element_order) ) end do end do return end subroutine r8ge_fss ( n, a, nb, b, info ) !*****************************************************************************80 ! !! R8GE_FSS factors and solves multiple R8GE systems. ! ! Discussion: ! ! The R8GE storage format is used for a general M by N matrix. A storage ! space is made for each entry. The two dimensional logical ! array can be thought of as a vector of M*N entries, starting with ! the M entries in the column 1, then the M entries in column 2 ! and so on. Considered as a vector, the entry A(I,J) is then stored ! in vector location I+(J-1)*M. ! ! R8GE storage is used by LINPACK and LAPACK. ! ! This routine does not save the LU factors of the matrix, and hence cannot ! be used to efficiently solve multiple linear systems, or even to ! factor A at one time, and solve a single linear system at a later time. ! ! This routine uses partial pivoting, but no pivot vector is required. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 23 June 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the order of the matrix. ! N must be positive. ! ! Input/output, real ( kind = 8 ) A(N,N). ! On input, A is the coefficient matrix of the linear system. ! On output, A is in unit upper triangular form, and ! represents the U factor of an LU factorization of the ! original coefficient matrix. ! ! Input, integer ( kind = 4 ) NB, the number of right hand sides. ! ! Input/output, real ( kind = 8 ) B(N,NB). ! On input, the right hand sides of the linear system. ! On output, the solutions of the linear systems. ! ! Output, integer ( kind = 4 ) INFO, singularity flag. ! 0, no singularity detected. ! nonzero, the factorization failed on the INFO-th step. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) nb real ( kind = 8 ) a(n,n) real ( kind = 8 ) b(n,nb) integer ( kind = 4 ) i integer ( kind = 4 ) info integer ( kind = 4 ) ipiv integer ( kind = 4 ) j integer ( kind = 4 ) jcol real ( kind = 8 ) piv real ( kind = 8 ) row(n) real ( kind = 8 ) t(nb) real ( kind = 8 ) temp info = 0 do jcol = 1, n ! ! Find the maximum element in column I. ! piv = abs ( a(jcol,jcol) ) ipiv = jcol do i = jcol + 1, n if ( piv < abs ( a(i,jcol) ) ) then piv = abs ( a(i,jcol) ) ipiv = i end if end do if ( piv == 0.0D+00 ) then info = jcol write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8GE_FSS - Fatal error!' write ( *, '(a,i8)' ) ' Zero pivot on step ', info stop end if ! ! Switch rows JCOL and IPIV, and B. ! if ( jcol /= ipiv ) then row(1:n) = a(jcol,1:n) a(jcol,1:n) = a(ipiv,1:n) a(ipiv,1:n) = row(1:n) t(1:nb) = b(jcol,1:nb) b(jcol,1:nb) = b(ipiv,1:nb) b(ipiv,1:nb) = t(1:nb) end if ! ! Scale the pivot row. ! a(jcol,jcol+1:n) = a(jcol,jcol+1:n) / a(jcol,jcol) b(jcol,1:nb) = b(jcol,1:nb) / a(jcol,jcol) a(jcol,jcol) = 1.0D+00 ! ! Use the pivot row to eliminate lower entries in that column. ! do i = jcol + 1, n if ( a(i,jcol) /= 0.0D+00 ) then temp = - a(i,jcol) a(i,jcol) = 0.0D+00 a(i,jcol+1:n) = a(i,jcol+1:n) + temp * a(jcol,jcol+1:n) b(i,1:nb) = b(i,1:nb) + temp * b(jcol,1:nb) end if end do end do ! ! Back solve. ! do j = 1, nb do jcol = n, 2, -1 b(1:jcol-1,j) = b(1:jcol-1,j) - a(1:jcol-1,jcol) * b(jcol,j) end do end do return end subroutine r8mat_data_read ( input_file_name, m, n, table ) !*****************************************************************************80 ! !! R8MAT_DATA_READ reads data from an R8MAT file. ! ! Discussion: ! ! The file may contain more than N points, but this routine will ! return after reading N of them. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 18 October 2008 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the input file. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Output, real ( kind = 8 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) ierror character ( len = * ) input_file_name integer ( kind = 4 ) input_status integer ( kind = 4 ) input_unit integer ( kind = 4 ) j character ( len = 255 ) line real ( kind = 8 ) table(m,n) real ( kind = 8 ) x(m) ierror = 0 call get_unit ( input_unit ) open ( unit = input_unit, file = input_file_name, status = 'old', & iostat = input_status ) if ( input_status /= 0 ) then ierror = 1 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_DATA_READ - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the input file "' // & trim ( input_file_name ) // '" on unit ', input_unit stop end if j = 0 do while ( j < n ) read ( input_unit, '(a)', iostat = input_status ) line if ( input_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_DATA_READ - Fatal error!' write ( *, '(a)' ) ' Error while reading lines of data.' write ( *, '(a,i8)' ) ' Number of values expected per line M = ', m write ( *, '(a,i8)' ) ' Number of data lines read, J = ', j write ( *, '(a,i8)' ) ' Number of data lines needed, N = ', n stop end if if ( line(1:1) == '#' .or. len_trim ( line ) == 0 ) then cycle end if call s_to_r8vec ( line, m, x, ierror ) if ( ierror /= 0 ) then cycle end if j = j + 1 table(1:m,j) = x(1:m) end do close ( unit = input_unit ) return end subroutine r8mat_header_read ( input_file_name, m, n ) !*****************************************************************************80 ! !! R8MAT_HEADER_READ reads the header from an R8MAT file. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) INPUT_FILE_NAME, the name of the input file. ! ! Output, integer ( kind = 4 ) M, spatial dimension. ! ! Output, integer ( kind = 4 ) N, the number of points. ! implicit none character ( len = * ) input_file_name integer ( kind = 4 ) m integer ( kind = 4 ) n call file_column_count ( input_file_name, m ) if ( m <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data columns in' write ( *, '(a)' ) ' the file "' // trim ( input_file_name ) // '".' stop end if call file_row_count ( input_file_name, n ) if ( n <= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_HEADER_READ - Fatal error!' write ( *, '(a)' ) ' There was some kind of I/O problem while trying' write ( *, '(a)' ) ' to count the number of data rows in' write ( *, '(a)' ) ' the file "' // trim ( input_file_name ) // '".' stop end if return end subroutine r8mat_write ( output_file_name, m, n, table ) !*****************************************************************************80 ! !! R8MAT_WRITE writes an R8MAT file. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 31 May 2009 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) OUTPUT_FILE_NAME, the output file name. ! ! Input, integer ( kind = 4 ) M, the spatial dimension. ! ! Input, integer ( kind = 4 ) N, the number of points. ! ! Input, real ( kind = 8 ) TABLE(M,N), the table data. ! implicit none integer ( kind = 4 ) m integer ( kind = 4 ) n integer ( kind = 4 ) j character ( len = * ) output_file_name integer ( kind = 4 ) output_status integer ( kind = 4 ) output_unit character ( len = 30 ) string real ( kind = 8 ) table(m,n) ! ! Open the file. ! call get_unit ( output_unit ) open ( unit = output_unit, file = output_file_name, & status = 'replace', iostat = output_status ) if ( output_status /= 0 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'R8MAT_WRITE - Fatal error!' write ( *, '(a,i8)' ) ' Could not open the output file "' // & trim ( output_file_name ) // '" on unit ', output_unit output_unit = -1 stop end if ! ! Create a format string. ! ! For greater precision in the output file, try: ! ! '(', m, 'g', 24, '.', 16, ')' ! write ( string, '(a1,i8,a1,i8,a1,i8,a1)' ) '(', m, 'g', 14, '.', 6, ')' ! ! Write the data. ! do j = 1, n write ( output_unit, string ) table(1:m,j) end do ! ! Close the file. ! close ( unit = output_unit ) return end subroutine s_to_i4 ( s, ival, ierror, length ) !*****************************************************************************80 ! !! S_TO_I4 reads an I4 from a string. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 28 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, a string to be examined. ! ! Output, integer ( kind = 4 ) IVAL, the integer value read from the string. ! If the string is blank, then IVAL will be returned 0. ! ! Output, integer ( kind = 4 ) IERROR, an error flag. ! 0, no error. ! 1, an error occurred. ! ! Output, integer ( kind = 4 ) LENGTH, the number of characters of S ! used to make IVAL. ! implicit none character c integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) isgn integer ( kind = 4 ) istate integer ( kind = 4 ) ival integer ( kind = 4 ) length character ( len = * ) s ierror = 0 istate = 0 isgn = 1 ival = 0 do i = 1, len_trim ( s ) c = s(i:i) ! ! Haven't read anything. ! if ( istate == 0 ) then if ( c == ' ' ) then else if ( c == '-' ) then istate = 1 isgn = -1 else if ( c == '+' ) then istate = 1 isgn = + 1 else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read the sign, expecting digits. ! else if ( istate == 1 ) then if ( c == ' ' ) then else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then istate = 2 ival = ichar ( c ) - ichar ( '0' ) else ierror = 1 return end if ! ! Have read at least one digit, expecting more. ! else if ( istate == 2 ) then if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then ival = 10 * ival + ichar ( c ) - ichar ( '0' ) else ival = isgn * ival length = i - 1 return end if end if end do ! ! If we read all the characters in the string, see if we're OK. ! if ( istate == 2 ) then ival = isgn * ival length = len_trim ( s ) else ierror = 1 length = 0 end if return end subroutine s_to_i4vec ( s, n, ivec, ierror ) !*****************************************************************************80 ! !! S_TO_I4VEC reads an I4VEC from a string. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 08 October 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer ( kind = 4 ) N, the number of values expected. ! ! Output, integer ( kind = 4 ) IVEC(N), the values read from the string. ! ! Output, integer ( kind = 4 ) IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) ilo integer ( kind = 4 ) ivec(n) integer ( kind = 4 ) length character ( len = * ) s i = 0 ierror = 0 ilo = 1 do while ( i < n ) i = i + 1 call s_to_i4 ( s(ilo:), ivec(i), ierror, length ) if ( ierror /= 0 ) then ierror = -i exit end if ilo = ilo + length end do return end subroutine s_to_r8 ( s, dval, ierror, length ) !*****************************************************************************80 ! !! S_TO_R8 reads an R8 from a string. ! ! Discussion: ! ! The routine will read as many characters as possible until it reaches ! the end of the string, or encounters a character which cannot be ! part of the number. ! ! Legal input is: ! ! 1 blanks, ! 2 '+' or '-' sign, ! 2.5 blanks ! 3 integer part, ! 4 decimal point, ! 5 fraction part, ! 6 'E' or 'e' or 'D' or 'd', exponent marker, ! 7 exponent sign, ! 8 exponent integer part, ! 9 exponent decimal point, ! 10 exponent fraction part, ! 11 blanks, ! 12 final comma or semicolon, ! ! with most quantities optional. ! ! Example: ! ! S DVAL ! ! '1' 1.0 ! ' 1 ' 1.0 ! '1A' 1.0 ! '12,34,56' 12.0 ! ' 34 7' 34.0 ! '-1E2ABCD' -100.0 ! '-1X2ABCD' -1.0 ! ' 2E-1' 0.2 ! '23.45' 23.45 ! '-4.2E+2' -420.0 ! '17d2' 1700.0 ! '-14e-2' -0.14 ! 'e2' 100.0 ! '-12.73e-9.23' -12.73 * 10.0**(-9.23) ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string containing the ! data to be read. Reading will begin at position 1 and ! terminate at the end of the string, or when no more ! characters can be read to form a legal real. Blanks, ! commas, or other nonnumeric data will, in particular, ! cause the conversion to halt. ! ! Output, real ( kind = 8 ) DVAL, the value read from the string. ! ! Output, integer ( kind = 4 ) IERROR, error flag. ! 0, no errors occurred. ! 1, 2, 6 or 7, the input number was garbled. The ! value of IERROR is the last type of input successfully ! read. For instance, 1 means initial blanks, 2 means ! a plus or minus sign, and so on. ! ! Output, integer ( kind = 4 ) LENGTH, the number of characters read ! to form the number, including any terminating ! characters such as a trailing comma or blanks. ! implicit none character c logical ch_eqi real ( kind = 8 ) dval integer ( kind = 4 ) ierror integer ( kind = 4 ) ihave integer ( kind = 4 ) isgn integer ( kind = 4 ) iterm integer ( kind = 4 ) jbot integer ( kind = 4 ) jsgn integer ( kind = 4 ) jtop integer ( kind = 4 ) length integer ( kind = 4 ) nchar integer ( kind = 4 ) ndig real ( kind = 8 ) rbot real ( kind = 8 ) rexp real ( kind = 8 ) rtop character ( len = * ) s nchar = len_trim ( s ) ierror = 0 dval = 0.0D+00 length = -1 isgn = 1 rtop = 0 rbot = 1 jsgn = 1 jtop = 0 jbot = 1 ihave = 1 iterm = 0 do length = length + 1 if ( nchar < length+1 ) then exit end if c = s(length+1:length+1) ! ! Blank character. ! if ( c == ' ' ) then if ( ihave == 2 ) then else if ( ihave == 6 .or. ihave == 7 ) then iterm = 1 else if ( 1 < ihave ) then ihave = 11 end if ! ! Comma. ! else if ( c == ',' .or. c == ';' ) then if ( ihave /= 1 ) then iterm = 1 ihave = 12 length = length + 1 end if ! ! Minus sign. ! else if ( c == '-' ) then if ( ihave == 1 ) then ihave = 2 isgn = -1 else if ( ihave == 6 ) then ihave = 7 jsgn = -1 else iterm = 1 end if ! ! Plus sign. ! else if ( c == '+' ) then if ( ihave == 1 ) then ihave = 2 else if ( ihave == 6 ) then ihave = 7 else iterm = 1 end if ! ! Decimal point. ! else if ( c == '.' ) then if ( ihave < 4 ) then ihave = 4 else if ( 6 <= ihave .and. ihave <= 8 ) then ihave = 9 else iterm = 1 end if ! ! Scientific notation exponent marker. ! else if ( ch_eqi ( c, 'E' ) .or. ch_eqi ( c, 'D' ) ) then if ( ihave < 6 ) then ihave = 6 else iterm = 1 end if ! ! Digit. ! else if ( ihave < 11 .and. lle ( '0', c ) .and. lle ( c, '9' ) ) then if ( ihave <= 2 ) then ihave = 3 else if ( ihave == 4 ) then ihave = 5 else if ( ihave == 6 .or. ihave == 7 ) then ihave = 8 else if ( ihave == 9 ) then ihave = 10 end if call ch_to_digit ( c, ndig ) if ( ihave == 3 ) then rtop = 10.0D+00 * rtop + real ( ndig, kind = 8 ) else if ( ihave == 5 ) then rtop = 10.0D+00 * rtop + real ( ndig, kind = 8 ) rbot = 10.0D+00 * rbot else if ( ihave == 8 ) then jtop = 10 * jtop + ndig else if ( ihave == 10 ) then jtop = 10 * jtop + ndig jbot = 10 * jbot end if ! ! Anything else is regarded as a terminator. ! else iterm = 1 end if ! ! If we haven't seen a terminator, and we haven't examined the ! entire string, go get the next character. ! if ( iterm == 1 ) then exit end if end do ! ! If we haven't seen a terminator, and we have examined the ! entire string, then we're done, and LENGTH is equal to NCHAR. ! if ( iterm /= 1 .and. length+1 == nchar ) then length = nchar end if ! ! Number seems to have terminated. Have we got a legal number? ! Not if we terminated in states 1, 2, 6 or 7! ! if ( ihave == 1 .or. ihave == 2 .or. ihave == 6 .or. ihave == 7 ) then ierror = ihave write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'S_TO_R8 - Serious error!' write ( *, '(a)' ) ' Illegal or nonnumeric input:' write ( *, '(a)' ) ' ' // trim ( s ) return end if ! ! Number seems OK. Form it. ! if ( jtop == 0 ) then rexp = 1.0D+00 else if ( jbot == 1 ) then rexp = 10.0D+00 ** ( jsgn * jtop ) else rexp = 10.0D+00 ** ( real ( jsgn * jtop, kind = 8 ) & / real ( jbot, kind = 8 ) ) end if end if dval = real ( isgn, kind = 8 ) * rexp * rtop / rbot return end subroutine s_to_r8vec ( s, n, rvec, ierror ) !*****************************************************************************80 ! !! S_TO_R8VEC reads an R8VEC from a string. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 07 September 2004 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be read. ! ! Input, integer ( kind = 4 ) N, the number of values expected. ! ! Output, real ( kind = 8 ) RVEC(N), the values read from the string. ! ! Output, integer ( kind = 4 ) IERROR, error flag. ! 0, no errors occurred. ! -K, could not read data for entries -K through N. ! implicit none integer ( kind = 4 ) n integer ( kind = 4 ) i integer ( kind = 4 ) ierror integer ( kind = 4 ) ilo integer ( kind = 4 ) lchar real ( kind = 8 ) rvec(n) character ( len = * ) s i = 0 ierror = 0 ilo = 1 do while ( i < n ) i = i + 1 call s_to_r8 ( s(ilo:), rvec(i), ierror, lchar ) if ( ierror /= 0 ) then ierror = -i exit end if ilo = ilo + lchar end do return end subroutine s_word_count ( s, nword ) !*****************************************************************************80 ! !! S_WORD_COUNT counts the number of "words" in a string. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 14 April 1999 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) S, the string to be examined. ! ! Output, integer ( kind = 4 ) NWORD, the number of "words" in the string. ! Words are presumed to be separated by one or more blanks. ! implicit none logical blank integer ( kind = 4 ) i integer ( kind = 4 ) lens integer ( kind = 4 ) nword character ( len = * ) s nword = 0 lens = len ( s ) if ( lens <= 0 ) then return end if blank = .true. do i = 1, lens if ( s(i:i) == ' ' ) then blank = .true. else if ( blank ) then nword = nword + 1 blank = .false. end if end do return end subroutine sort_heap_external ( n, indx, i, j, isgn ) !*****************************************************************************80 ! !! SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order. ! ! Discussion: ! ! The actual list of data is not passed to the routine. Hence this ! routine may be used to sort integers, real ( kind = 8 )s, numbers, names, ! dates, shoe sizes, and so on. After each call, the routine asks ! the user to compare or interchange two items, until a special ! return value signals that the sorting is completed. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 05 February 2004 ! ! Author: ! ! Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf. ! FORTRAN90 version by John Burkardt. ! ! Reference: ! ! Albert Nijenhuis, Herbert Wilf, ! Combinatorial Algorithms, ! Academic Press, 1978, second edition, ! ISBN 0-12-519260-6. ! ! Parameters: ! ! Input, integer ( kind = 4 ) N, the number of items to be sorted. ! ! Input/output, integer ( kind = 4 ) INDX, the main communication signal. ! ! The user must set INDX to 0 before the first call. ! Thereafter, the user should not change the value of INDX until ! the sorting is done. ! ! On return, if INDX is ! ! greater than 0, ! * interchange items I and J; ! * call again. ! ! less than 0, ! * compare items I and J; ! * set ISGN = -1 if I < J, ISGN = +1 if J < I; ! * call again. ! ! equal to 0, the sorting is done. ! ! Output, integer ( kind = 4 ) I, J, the indices of two items. ! On return with INDX positive, elements I and J should be interchanged. ! On return with INDX negative, elements I and J should be compared, and ! the result reported in ISGN on the next call. ! ! Input, integer ( kind = 4 ) ISGN, results of comparison of elements I ! and J. (Used only when the previous call returned INDX less than 0). ! ISGN <= 0 means I is less than or equal to J; ! 0 <= ISGN means I is greater than or equal to J. ! implicit none integer ( kind = 4 ) i integer ( kind = 4 ), save :: i_save = 0 integer ( kind = 4 ) indx integer ( kind = 4 ) isgn integer ( kind = 4 ) j integer ( kind = 4 ), save :: j_save = 0 integer ( kind = 4 ), save :: k = 0 integer ( kind = 4 ), save :: k1 = 0 integer ( kind = 4 ) n integer ( kind = 4 ), save :: n1 = 0 ! ! INDX = 0: This is the first call. ! if ( indx == 0 ) then i_save = 0 j_save = 0 k = n / 2 k1 = k n1 = n ! ! INDX < 0: The user is returning the results of a comparison. ! else if ( indx < 0 ) then if ( indx == -2 ) then if ( isgn < 0 ) then i_save = i_save + 1 end if j_save = k1 k1 = i_save indx = -1 i = i_save j = j_save return end if if ( 0 < isgn ) then indx = 2 i = i_save j = j_save return end if if ( k <= 1 ) then if ( n1 == 1 ) then i_save = 0 j_save = 0 indx = 0 else i_save = n1 n1 = n1 - 1 j_save = 1 indx = 1 end if i = i_save j = j_save return end if k = k - 1 k1 = k ! ! 0 < INDX, the user was asked to make an interchange. ! else if ( indx == 1 ) then k1 = k end if do i_save = 2 * k1 if ( i_save == n1 ) then j_save = k1 k1 = i_save indx = -1 i = i_save j = j_save return else if ( i_save <= n1 ) then j_save = i_save + 1 indx = -2 i = i_save j = j_save return end if if ( k <= 1 ) then exit end if k = k - 1 k1 = k end do if ( n1 == 1 ) then i_save = 0 j_save = 0 indx = 0 i = i_save j = j_save else i_save = n1 n1 = n1 - 1 j_save = 1 indx = 1 i = i_save j = j_save end if return end subroutine timestamp ( ) !*****************************************************************************80 ! !! TIMESTAMP prints the current YMDHMS date as a time stamp. ! ! Example: ! ! 31 May 2001 9:45:54.872 AM ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 18 May 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none character ( len = 8 ) ampm integer ( kind = 4 ) d integer ( kind = 4 ) h integer ( kind = 4 ) m integer ( kind = 4 ) mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer ( kind = 4 ) n integer ( kind = 4 ) s integer ( kind = 4 ) values(8) integer ( kind = 4 ) y call date_and_time ( values = values ) y = values(1) m = values(2) d = values(3) h = values(5) n = values(6) s = values(7) mm = values(8) if ( h < 12 ) then ampm = 'AM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Noon' else ampm = 'PM' end if else h = h - 12 if ( h < 12 ) then ampm = 'PM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Midnight' else ampm = 'AM' end if end if end if write ( *, '(i2.2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) & d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm ) return end subroutine triangulation_order3_neighbor_triangles ( triangle_num, & triangle_node, triangle_neighbor ) !*****************************************************************************80 ! !! TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors. ! ! Discussion: ! ! A triangulation of a set of nodes can be completely described by ! the coordinates of the nodes, and the list of nodes that make up ! each triangle. However, in some cases, it is necessary to know ! triangle adjacency information, that is, which triangle, if any, ! is adjacent to a given triangle on a particular side. ! ! This routine creates a data structure recording this information. ! ! The primary amount of work occurs in sorting a list of 3 * TRIANGLE_NUM ! data items. ! ! Note that ROW is a work array allocated dynamically inside this ! routine. It is possible, for very large values of TRIANGLE_NUM, ! that the necessary amount of memory will not be accessible, and the ! routine will fail. This is a limitation of the implementation of ! dynamic arrays in FORTRAN90. One way to get around this would be ! to require the user to declare ROW in the calling routine ! as an allocatable array, get the necessary memory explicitly with ! an ALLOCATE statement, and then pass ROW into this routine. ! ! Of course, the point of dynamic arrays was to make it easy to ! hide these sorts of temporary work arrays from the poor user! ! ! This routine was revised to store the edge data in a column ! array rather than a row array. ! ! Example: ! ! The input information from TRIANGLE_NODE: ! ! Triangle Nodes ! -------- --------------- ! 1 3 4 1 ! 2 3 1 2 ! 3 3 2 8 ! 4 2 1 5 ! 5 8 2 13 ! 6 8 13 9 ! 7 3 8 9 ! 8 13 2 5 ! 9 9 13 7 ! 10 7 13 5 ! 11 6 7 5 ! 12 9 7 6 ! 13 10 9 6 ! 14 6 5 12 ! 15 11 6 12 ! 16 10 6 11 ! ! The output information in TRIANGLE_NEIGHBOR: ! ! Triangle Neighboring Triangles ! -------- --------------------- ! ! 1 -1 -1 2 ! 2 1 4 3 ! 3 2 5 7 ! 4 2 -1 8 ! 5 3 8 6 ! 6 5 9 7 ! 7 3 6 -1 ! 8 5 4 10 ! 9 6 10 12 ! 10 9 8 11 ! 11 12 10 14 ! 12 9 11 13 ! 13 -1 12 16 ! 14 11 -1 15 ! 15 16 14 -1 ! 16 13 15 -1 ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 14 February 2006 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer ( kind = 4 ) TRIANGLE_NUM, the number of triangles. ! ! Input, integer ( kind = 4 ) TRIANGLE_NODE(3,TRIANGLE_NUM), the nodes ! that make up each triangle. ! ! Output, integer ( kind = 4 ) TRIANGLE_NEIGHBOR(3,TRIANGLE_NUM), the three ! triangles that are direct neighbors of a given triangle. ! TRIANGLE_NEIGHBOR(1,I) is the index of the triangle which touches side 1, ! defined by nodes 2 and 3, and so on. TRIANGLE_NEIGHBOR(1,I) is negative ! if there is no neighbor on that side. In this case, that side of the ! triangle lies on the boundary of the triangulation. ! implicit none integer ( kind = 4 ) triangle_num integer ( kind = 4 ), parameter :: triangle_order = 3 integer ( kind = 4 ) col(4,3*triangle_num) integer ( kind = 4 ) i integer ( kind = 4 ) icol integer ( kind = 4 ) j integer ( kind = 4 ) k integer ( kind = 4 ) side1 integer ( kind = 4 ) side2 integer ( kind = 4 ) triangle_neighbor(3,triangle_num) integer ( kind = 4 ) tri integer ( kind = 4 ) triangle_node(triangle_order,triangle_num) integer ( kind = 4 ) tri1 integer ( kind = 4 ) tri2 ! ! Step 1. ! From the list of nodes for triangle T, of the form: (I,J,K) ! construct the three neighbor relations: ! ! (I,J,1,T) or (J,I,1,T), ! (J,K,2,T) or (K,J,2,T), ! (K,I,3,T) or (I,K,3,T) ! ! where we choose (I,J,1,T) if I < J, or else (J,I,1,T) ! do tri = 1, triangle_num i = triangle_node(1,tri) j = triangle_node(2,tri) k = triangle_node(3,tri) if ( i < j ) then col(1:4,3*(tri-1)+1) = (/ i, j, 1, tri /) else col(1:4,3*(tri-1)+1) = (/ j, i, 1, tri /) end if if ( j < k ) then col(1:4,3*(tri-1)+2) = (/ j, k, 2, tri /) else col(1:4,3*(tri-1)+2) = (/ k, j, 2, tri /) end if if ( k < i ) then col(1:4,3*(tri-1)+3) = (/ k, i, 3, tri /) else col(1:4,3*(tri-1)+3) = (/ i, k, 3, tri /) end if end do ! ! Step 2. Perform an ascending dictionary sort on the neighbor relations. ! We only intend to sort on rows 1 and 2; the routine we call here ! sorts on rows 1 through 4 but that won't hurt us. ! ! What we need is to find cases where two triangles share an edge. ! Say they share an edge defined by the nodes I and J. Then there are ! two columns of COL that start out ( I, J, ?, ? ). By sorting COL, ! we make sure that these two columns occur consecutively. That will ! make it easy to notice that the triangles are neighbors. ! call i4col_sort_a ( 4, 3*triangle_num, col ) ! ! Step 3. Neighboring triangles show up as consecutive columns with ! identical first two entries. Whenever you spot this happening, ! make the appropriate entries in TRIANGLE_NEIGHBOR. ! triangle_neighbor(1:3,1:triangle_num) = -1 icol = 1 do if ( 3 * triangle_num <= icol ) then exit end if if ( col(1,icol) /= col(1,icol+1) .or. col(2,icol) /= col(2,icol+1) ) then icol = icol + 1 cycle end if side1 = col(3,icol) tri1 = col(4,icol) side2 = col(3,icol+1) tri2 = col(4,icol+1) triangle_neighbor(side1,tri1) = tri2 triangle_neighbor(side2,tri2) = tri1 icol = icol + 2 end do return end subroutine triangulation_search_delaunay ( node_num, node_xy, triangle_order, & triangle_num, triangle_node, triangle_neighbor, p, triangle_index, edge ) !*****************************************************************************80 ! !! TRIANGULATION_SEARCH_DELAUNAY searches a Delaunay triangulation for a point. ! ! Discussion: ! ! The algorithm "walks" from one triangle to its neighboring triangle, ! and so on, until a triangle is found containing point P, or P is found ! to be outside the convex hull. ! ! The algorithm computes the barycentric coordinates of the point with ! respect to the current triangle. If all three quantities are positive, ! the point is contained in the triangle. If the I-th coordinate is ! negative, then P lies on the far side of edge I, which is opposite ! from vertex I. This gives a hint as to where to search next. ! ! For a Delaunay triangulation, the search is guaranteed to terminate. ! For other triangulations, a cycle may occur. ! ! Note the surprising fact that, even for a Delaunay triangulation of ! a set of nodes, the nearest node to P need not be one of the ! vertices of the triangle containing P. ! ! The code can be called for triangulations of any order, but only ! the first three nodes in each triangle are considered. Thus, if ! higher order triangles are used, and the extra nodes are intended ! to give the triangle a polygonal shape, these will have no effect, ! and the results obtained here might be misleading. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 01 August 2009 ! ! Author: ! ! Original FORTRAN77 version by Barry Joe. ! FORTRAN90 version by John Burkardt. ! ! Reference: ! ! Barry Joe, ! GEOMPACK - a software package for the generation of meshes ! using geometric algorithms, ! Advances in Engineering Software, ! Volume 13, pages 325-331, 1991. ! ! Parameters: ! ! Input, integer ( kind = 4 ) NODE_NUM, the number of nodes. ! ! Input, real ( kind = 8 ) NODE_XY(2,NODE_NUM), the coordinates of the nodes. ! ! Input, integer ( kind = 4 ) TRIANGLE_ORDER, the order of the triangles. ! ! Input, integer ( kind = 4 ) TRIANGLE_NUM, the number of triangles. ! ! Input, integer ( kind = 4 ) TRIANGLE_NODE(TRIANGLE_ORDER,TRIANGLE_NUM), ! the nodes that make up each triangle. ! ! Input, integer ( kind = 4 ) TRIANGLE_NEIGHBOR(3,TRIANGLE_NUM), the ! triangle neighbor list. ! ! Input, real ( kind = 8 ) P(2), the coordinates of a point. ! ! Output, integer ( kind = 4 ) TRIANGLE_INDEX, the index of the triangle ! where the search ended. If a cycle occurred, then TRIANGLE_INDEX = -1. ! ! Output, integer ( kind = 4 ) EDGE, indicates the position of the point P in ! triangle TRIANGLE_INDEX: ! 0, the interior or boundary of the triangle; ! -1, outside the convex hull of the triangulation, past edge 1; ! -2, outside the convex hull of the triangulation, past edge 2; ! -3, outside the convex hull of the triangulation, past edge 3. ! implicit none integer ( kind = 4 ), parameter :: dim_num = 2 integer ( kind = 4 ) node_num integer ( kind = 4 ) triangle_num integer ( kind = 4 ) triangle_order integer ( kind = 4 ) a real ( kind = 8 ) alpha integer ( kind = 4 ) b real ( kind = 8 ) beta integer ( kind = 4 ) c integer ( kind = 4 ) count real ( kind = 8 ) det real ( kind = 8 ) dxp real ( kind = 8 ) dxa real ( kind = 8 ) dxb real ( kind = 8 ) dyp real ( kind = 8 ) dya real ( kind = 8 ) dyb integer ( kind = 4 ) edge real ( kind = 8 ) gamma real ( kind = 8 ) node_xy(dim_num,node_num) real ( kind = 8 ) p(dim_num) integer ( kind = 4 ) triangle_node(triangle_order,triangle_num) integer ( kind = 4 ) triangle_index integer ( kind = 4 ), save :: triangle_index_save = -1 integer ( kind = 4 ) triangle_neighbor(3,triangle_num) ! ! If possible, start with the previous successful value of TRIANGLE_INDEX. ! if ( triangle_index_save < 1 .or. triangle_num < triangle_index_save ) then triangle_index = ( triangle_num + 1 ) / 2 else triangle_index = triangle_index_save end if count = 0 edge = 0 do count = count + 1 if ( triangle_num < count ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGULATION_SEARCH_DELAUNAY - Fatal error!' write ( *, '(a)' ) ' The algorithm seems to be cycling.' triangle_index = -1 edge = -1 stop end if ! ! Get the nodes of triangle TRIANGLE_INDEX. ! a = triangle_node(1,triangle_index) b = triangle_node(2,triangle_index) c = triangle_node(3,triangle_index) ! ! Using vertex C as a base, compute the distances to vertices A and B, ! and the point P. ! dxa = node_xy(1,a) - node_xy(1,c) dya = node_xy(2,a) - node_xy(2,c) dxb = node_xy(1,b) - node_xy(1,c) dyb = node_xy(2,b) - node_xy(2,c) dxp = p(1) - node_xy(1,c) dyp = p(2) - node_xy(2,c) det = dxa * dyb - dya * dxb ! ! Compute the barycentric coordinates of the point P with respect ! to this triangle. ! alpha = ( dxp * dyb - dyp * dxb ) / det beta = ( dxa * dyp - dya * dxp ) / det gamma = 1.0D+00 - alpha - beta ! ! If the barycentric coordinates are all positive, then the point ! is inside the triangle and we're done. ! if ( 0.0D+00 <= alpha .and. & 0.0D+00 <= beta .and. & 0.0D+00 <= gamma ) then exit end if ! ! At least one barycentric coordinate is negative. ! ! If there is a negative barycentric coordinate for which there exists ! an opposing triangle neighbor closer to the point, move to that triangle. ! ! (Two coordinates could be negative, in which case we could go for the ! most negative one, or the most negative one normalized by the actual ! distance it represents). ! if ( alpha < 0.0D+00 .and. 0 < triangle_neighbor(2,triangle_index) ) then triangle_index = triangle_neighbor(2,triangle_index) cycle else if ( beta < 0.0D+00 .and. & 0 < triangle_neighbor(3,triangle_index) ) then triangle_index = triangle_neighbor(3,triangle_index) cycle else if ( gamma < 0.0D+00 .and. & 0 < triangle_neighbor(1,triangle_index) ) then triangle_index = triangle_neighbor(1,triangle_index) cycle end if ! ! All negative barycentric coordinates correspond to vertices opposite ! sides on the convex hull. ! ! Note the edge and exit. ! if ( alpha < 0.0D+00 ) then edge = -2 exit else if ( beta < 0.0D+00 ) then edge = -3 exit else if ( gamma < 0.0D+00 ) then edge = -1 exit end if end do triangle_index_save = triangle_index return end